A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?

Answer:

[tex]\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]

Step-by-step explanation:

Perform the partial fraction decomposition

[tex]\int{\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)} } \, dx\\ \\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\ \\7x^3+5x^2+49x+5=(x^2+7)(Ax+B)+(x^2+1)(Cx+D)\\\\7x^3+5x^2+49x+5=Ax^3+Bx^2+7Ax+7B+Cx^3+Dx^2+Cx+D\\\\7x^3+5x^2+49x+5=Ax^3+Cx^3+Bx^2+Dx^2+7Ax+Cx+7B+D\\\\7x^3+5x^2+49x+5=x^3(A+C)+x^2(B+D)+x(7A+C)+7B+D[/tex]

Set up a system of equations and solve for each constant

[tex]\begin{cases} A + C = 7\\B + D = 5\\7 A + C = 49\\7 B + D = 5 \end{cases}[/tex]

[tex]A+C=7\\A=7-C[/tex]

[tex]7A+C=49\\7(7-C)+C=49\\49-7C+C=49\\49-6C=49\\-6C=0\\C=0[/tex]

[tex]A=7-C\\A=7-0\\A=7[/tex]

[tex]B+D=5\\B=5-D[/tex]

[tex]7B+D=5\\7(5-D)+D=5\\35-7D+D=5\\35-6D=5\\-6D=-30\\D=5[/tex]

[tex]B=5-D\\B=5-5\\B=0[/tex]

Plug solved constants in and evaluate

[tex]\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x+0}{x^2+1}+\frac{0x+5}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x}{x^2+1}+\frac{5}{x^2+7}[/tex]

Break up integral

[tex]\int {\bigr(\frac{7x}{x^2+1}+\frac{5}{x^2+7}\bigr) } \, dx[/tex]

[tex]\int {\frac{7x}{x^2+1} } \, dx +\int {\frac{5}{x^2+7}} \, dx\\\\\int {\frac{7x}{x^2+1} } \, dx +5\int {\frac{1}{x^2+7}} \, dx[/tex]

Solve first integral

Let [tex]u=x^2+1[/tex] and [tex]du=2xdx[/tex] for the first integral. Thus, [tex]\frac{7}{2}du=7xdx[/tex]:

[tex]\frac{7}{2}\int {\frac{du}{u}}\\\\\frac{7}{2}ln(|u|)+C\\ \\\frac{7}{2}ln(|x^2+1|)+C[/tex]

Solve second integral

Since [tex]5\int {\frac{1}{x^2+7} } \, dx[/tex] is in the form of [tex]\int{\frac{1}{x^2+a^2} } \, dx[/tex], its formula is [tex]\frac{1}{a}arctan(\frac{x}{a})+C[/tex]:

[tex]5\int {\frac{1}{x^2+7} } \, dx\\\\5\bigr(\frac{1}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\bigr)\\\\\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]

Combine integrals

[tex]\biggr[\frac{7}{2}ln(|x^2+1|)+C\biggr]+\biggr[\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\biggr]\\ \\\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]

Answer:

3=x+5

Step-by-step explanation:

Answer:

x + 5 = 3

Step-by-step explanation:

"Three is 5 more than a number."

The word is indicates that 3 is the final number, or rather, what the equation equals.

Then, 5 more than a number, shows the rest of your equation. A number is just your variable, so any letter. We'll use X. Then, it says that the answer (3) is 5 more than x. So, your equation is:

x + 5 = 3

Answer:

Step-by-step explanation:

a = 5, b = -7 c = 1

[tex]x=\frac{-b\pm\sqrt{{b^2-4ac}}}{2a}\\=\frac{-(-7)\pm\sqrt{{(-7)^2-4(5)(1)}}}{2(5)}\\\\=\frac{{7}\pm\sqrt{{49-20}}}{10}\\\\\\=\frac{{7}\pm\sqrt{{29}}}{10}\\\\[/tex]

so

[tex]x_1=\frac{7+\sqrt{29}}{10}\\x_2=\frac{7-\sqrt{29}}{10}[/tex]

Answer:

It depends on the gender of those 2 newborn rabbits

Step-by-step explanation:

It seems that the answer is anywhere between 130 and 150

Answer:

[tex]x=7+\sqrt{3},\:x=7-\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\mathrm{Switch\:sides}[/tex]

[tex]x^2-14x+46=0[/tex]

[tex]\mathrm{Solve\;wit\;Quadratic\;formula}[/tex]

[tex]x_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:46}}{2\cdot \:1}[/tex]

[tex]\sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:46}}{2\cdot \:1}=2\sqrt{3}[/tex]

[tex]x_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{3}}{2\cdot \:1}[/tex]

[tex]\mathrm{Separate\:the\:solutions}[/tex]

[tex]x_1=\frac{-\left(-14\right)+2\sqrt{3}}{2\cdot \:1},\:x_2=\frac{-\left(-14\right)-2\sqrt{3}}{2\cdot \:1}[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]

[tex]x=7+\sqrt{3},\:x=7-\sqrt{3}[/tex]

~Lenvy~

The number of people left out of 50 will be 20.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that 50 people went to a play [tex]\dfrac{3}{5}[/tex] of the people stayed to the end.

The number of people stays is calculated as:-

[tex]\rm\ N = 50 \times \dfrac{3}{5}[/tex]

N = 10 x 3

N = 30

The number of people left is calculated as:-

⇒ 50 - 30

⇒20

Therefore, the number of people left out of 50 will be 20.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ2

9514 1404 393

Answer:

  240

Step-by-step explanation:

Your calculator can tell you the answer.

__

If you're doing this by hand, it can be convenient to combine the multipliers of 48:

  (2 5/7)·48 +(2 2/7)·48 = (2 5/7 +2 2/7)·48 = ((2+2) +(5/7+2/7))·48

  = (4 +7/7)·48 = 5·48 = 240

Answer:

The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts. Suppose, x is the square root of y, then it is represented as x=√y or we can express the same equation as x2 = y. Here,'√'is the radical symbol used to represent the root of numbers.

Answer:

x = 10

Step-by-step explanation:

DE = EF, GE = GE, m∠D = m∠F = 90°

so

ΔDGE = ΔFGE

then

3x + 8 = 5x - 12

3x - 5x = -12 - 8

-2x = -20

2x = 20

x = 10

Step-by-step explanation:

Since DE=FE, we know GE is angle bisectors of angle G.

Thus, set those two expressions equal to each other.

3x+8= 5x-12

20=2x

x=10

Answer:

One notebook = $18.50

One pen= $1.10

18.50+1.10= $19.60

2) We must first set up an algebraic expression

total=15 pencils

total=9 pens

The total amount is the price of one pencil*15

To figure out one pencil:

10 pencils is $24

1 pencil is $2.40

Total= $36

9 pens = 36

Therefore 1 pen is $4

Step-by-step explanation:

1) We need to set up an algebraic expression to solve this problem:

Let n= cost of a notepad

Let p= cost of a pen

First set up an expression for Cynthia's purchase:

cost of notepads*number of notepads + cost of pens*number of pens = total cost

n*2 + p*3 = 40.30

Rewrite as:

2n + 3p = 40.30

Next, set up an expression for Annie's purchase:

Here we will be using the same variables

Again:

cost of notepads*number of notepads + cost of pens*number of pens = total cost

n*3 + p*5 = 61

Rewrite as:

3n + 5p =61

Now, set up a system of equations:

2n + 3p = 40.30

3n + 5p =61

A system of equations can be solved several ways, here I will use the addition/elimination method

For this method one of the variables must be able to be eliminated

Step 1: Pick a variable to eliminate

Here I will eliminate n

Step 2: make the selected variables in the equations equal and opposite so that they cancel out when the equations are added together

(2n + 3p = 40.30)(-3)

(3n + 5p =61)(2)

-6n - 9p = -120.90

6n + 10p = 122

Step 3: add vertically

-6n - 9p = -120.90

6n + 10p = 122

         p  =  1.10

Step 4: Figure out the other variable by inputting the answer you just got back into the original equation

2n + 3(1.10) = 40.30

2n + 3.30 = 40.30

      -3.30      37

         2n = 37

        /2     /2

         n = 18.5

Answer:

251.33cm³

Step-by-step explanation:

take pie as 22/7

surface area = 2π r h + 2π r²

2×22/7×5×3 + 2×22/7×5²

44/7×15 + 44/7×25

660/7 + 1100/7

660 + 1100 all over 7

= 1760/7

251.33cm³ Or 251.43cm³

Answer:

75%

Step-by-step explanation:

2.5 kilograms=2500 grams

2500-500=2000g to find the percent you devide 500/2500 then you get the percentage that was taken away so to find the percentage that was left you minus the 25 percent from 100 which gives you the answer which is 75%

Answer:

True

Step-by-step explanation:

(x + 4)² = (x + 4) (x + 4)

x² + 4² = x² + 16

Hello.

No, (x+4)² doesn't equal x²+16.

Let's see why.

Remember that

x times x = x²

4 times 4 = 4²=16

So it seems like (x+4)² is equal to x²+16.

However,

(x+4)²≠x²+16.

Well, what IS that equal to?

Turns out that

(x+4)² is equal to x² + twice the product of x and 4 +16 (!)

(x+4)²=x²+2*4*x+4²

(x+4)²=x²+8x+16

Therefore, (x+4)²=x²+8x+16.

I hope it helps.

Have an outstanding day. :)

[tex]\boxed{imperturbability}[/tex]

Answer:

  $77.76

Step-by-step explanation:

The future value formula is useful:

  FV = P(1 +r)^t

  FV = $45(1.20^3) = $45·1.728 = $77.76

Answer:

The answer is letter A

Step-by-step explanation:

Explanation:

The larger the confidence level, the wider the confidence interval gets. Choice A provides the largest such confidence level.

It's like trying to catch an elusive fish. The wider the net, the more confident that you are likely to catch the fish. The size of the net can be a sort of measure of the confidence level.

The confidence level that would produce the widest interval when estimating the mean of a population based on the mean and standard deviation of a sample of that population is 99%.

Option A is the correct answer.

A confidence interval is a statistical range that is used to estimate the true value of an unknown population parameter, such as a population means or proportion, based on a sample from that population.

The confidence interval provides a range of values that is likely to contain the true population parameter with a certain degree of confidence, which is typically expressed as a percentage.

We have,

The wider the interval, the lower the precision of the estimate, and the higher the confidence level, the wider the interval.

Therefore,

The confidence level that would produce the widest interval when estimating the mean of a population based on the mean and standard deviation of a sample of that population is 99%.

Learn more about confidence intervals here:

https://brainly.com/question/17212516

#SPJ7

Answer:

the smallest angle are 30 degree

Step-by-step explanation:

let x is the angle of triangle

x+2x+3x=180

6x=180

6x/6=180/6

x=30 degree

2x=60 degree

3x=90degree

Answer:

{A and B} = 0.20

{A and not B} = 0.24

{B and not A} = 0.06

{neither A nor B} = 0.50

Step-by-step explanation:

Given the following :

P(A) = 0.44

P(B) = 0.26

P(A or B) = 0.50.

{A and B} = 0.20

{A and not B} = 0.24

{B and not A} = 0.06

{neither A nor B} = 0.50

Kindly check attached picture for detailed explanation

The service charge without the VAT is  Rs. 2000.

VAT means value added tax. It is a form of tax levied on goods and services. Taxes are compulsory amounts or percentages that is levied on certain goods and services. Taxes increase the price of products.

Service charge = VAT / percentage VAT

260 / 13%

260 / 0.13 = Rs. 2000

To learn more about taxes, please check: https://brainly.com/question/25311567

Answer:

[tex]y = 0.04[/tex]

Step-by-step explanation:

[tex]y[/tex] ∝ [tex]\frac{k}{x}[/tex] (k is a constant we need)

[tex]12 = \frac{k}{20}[/tex]

[tex]k = 0.6[/tex]

[tex]y = \frac{0.6}{15}[/tex]

[tex]y=0.04[/tex]

Answer:

[tex]\frac{2}{3}[/tex] lbs per book

Step-by-step explanation:

     We can divide 4 pounds by the total number of books, 6, to find out how much each book weighs.

     4 lbs / 6 books = [tex]\frac{4/2}{6/2}=\frac{2}{3}[/tex] lbs

Each book weighs [tex]\frac{2}{3}[/tex] lbs

2/3 is equal to about 0.667

Another thing I wanted to note, 2 lbs * 6 = 12 lbs, not 10 lbs.

Answer:

The answer is 24

Step-by-step explanation:

Since the population after x hours is 2x, then after 12 hours, we'll substitute x = 12 into the function.

The population becomes 2 x 12 = 24

Answer:

b=0.7(3) The 3 in the parentheses means the 3 repeats forever

Step-by-step explanation:

If you simplify the sides, it will equal -1.5b=3b-3.3. This means that 4.5b=3.3. This means that b=0.7(3). The 3 will repeat forever.

Hopefully the explanation and the answer helps you!

Answer:

A:

625 in3 I think

ok so I think coz I'm in 4rth

Answer:

1st 306.36 2nd 10.78 3rd 355.25

Step-by-step explanation:

bc i just skipped and it showed me the answers

Answer: angle BEC = 43 degrees

Step-by-step explanation:

Straight angle = 180 degrees

75 + 62 = 137

180 - 137 = 43

Answer:

Simple, 4 sided polygon

Step-by-step explanation:

Here is the vocabulary:

A quadrilateral is a 4 sided shape, the prefix "quad" is meaning 4
Ex: Squares, Rhombus, Rectangles

A Triangle is a 3 sided polygon. The prefix "tri" means 3 like a tricycle.

Ex: Equilateral, Scalene, Isosceles, or right triangles

2 sided polygon is a digon that isn't used lots in basic geometry. The prefix di means 2.

Ex: Few examples but a common one is digon.

Answer:

The answer is 112

Step-by-step explanation:

Area= base + base divided by 2 times height.

So 12+16 divided by 2 times 8.